Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
*~*~*~*HELP PLEASE*~*~*~*
Factor 400x^2 + 160x + 16 completely.
 one year ago
 one year ago
*~*~*~*HELP PLEASE*~*~*~* Factor 400x^2 + 160x + 16 completely.
 one year ago
 one year ago

This Question is Closed

Steph_Rawr352Best ResponseYou've already chosen the best response.0
Oh.. and I have to factor it using a special product or something?
 one year ago

AylinBest ResponseYou've already chosen the best response.1
a=400, b=160, c=16 ac=6400 We need to find factors of 6400 that add up to 160 do start the problem.
 one year ago

AylinBest ResponseYou've already chosen the best response.1
Ok. Now we will form this square:\[\left[\begin{matrix}400x^{2} & 80x \\ 80x & 16\end{matrix}\right]\]Notice that ax^2 is the first element of the first row, c is the second element of the second row, and the two factors times x are the other two entries (it doesn't matter which spot you put the factors in). Now, the next step is to find the greatest common factors of each row and each column. For example, the row with 80x and 16 has 16 as its greatest common factor. (In your work write this in front of the that row. I would show you exactly what I mean, but I don't think the formatting here will let me do it.) Then do that with the rest of the rows and columns. Finally, take those factors that you found and they will be the factored solution. The factors for the columns will be one set of parenthesis, and the factors for the rows will be the other set.
 one year ago

rizwan_uetBest ResponseYou've already chosen the best response.0
400x^2 + 160x + 16 = (20x)^2 +160x+4^2 = (20x)^2 +2(20x)(4)+4^2 can you do it now??
 one year ago

rizwan_uetBest ResponseYou've already chosen the best response.0
hint: a^2+2ab+b^2 = (a+b)^2 = (a+b)(a+b)
 one year ago

AylinBest ResponseYou've already chosen the best response.1
The only other thing to expand it to a more general case (where you would say have negative factors or a is negative) is that the factor you write in front of the row or above the column has the same sign as the closest element to it. So for example if a was negative, the factor for that row would be negative, regardless of whether or not the other entry in that row was negative or positive. The same holds true for that column.
 one year ago

Steph_Rawr352Best ResponseYou've already chosen the best response.0
@Aylin I don't understand the square thing with the ax^2 and c? and @rizwan_uet where would you put the factors that add up to 160?
 one year ago

AylinBest ResponseYou've already chosen the best response.1
That's just a box you put the entries into to help with factoring.
 one year ago

AylinBest ResponseYou've already chosen the best response.1
When you have your final answer you can post it here and either I or rizwan should be able to tell you if it is correct or give some more help if needed.
 one year ago

Steph_Rawr352Best ResponseYou've already chosen the best response.0
ohk i will(: Thanks guys I wish I could pick 2 best answers
 one year ago

Steph_Rawr352Best ResponseYou've already chosen the best response.0
I got (20x + 4)^2
 one year ago

AylinBest ResponseYou've already chosen the best response.1
That does work, but it is not the simplest form. 20x and 4 both share a factor of 4. Do you know how to make it simpler?
 one year ago

Steph_Rawr352Best ResponseYou've already chosen the best response.0
so it would be 5x + 1?
 one year ago

AylinBest ResponseYou've already chosen the best response.1
Sort of. \[(20x+4)^{2}=(4(5x+1))^{2}=16(5x+1)^{2}\]
 one year ago

Steph_Rawr352Best ResponseYou've already chosen the best response.0
oh ohk thank you!!
 one year ago

rizwan_uetBest ResponseYou've already chosen the best response.0
you have this ok (20x)^2 +160x+4^2 now from the factors (20x)^2 and 4^2 i can write (20x)^2 +2(20x)(4)+4^2 because i know the formula a^2+2ab+b^2 = (a+b)^2 thus (20x)^2 +2(20x)(4)+4^2 = (20x+4)^2
 one year ago

rizwan_uetBest ResponseYou've already chosen the best response.0
now (20x+4)^2 = (20x+4)(20x+4) thus the required factors are (20x+4)(20x+4)
 one year ago

Steph_Rawr352Best ResponseYou've already chosen the best response.0
oh I understand now thank you so much!
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.